 Pupils practise counting 1, 2, 3… , ordering for example, first, second, third… , and to indicate a quantity for example, 3 apples, 2 centimetres , including solving simple concrete problems, until they are fluent. Pupils begin to recognise place value in numbers beyond 20 by reading, writing, counting and comparing numbers up to , supported by objects and pictorial representations.

They practise counting as reciting numbers and counting as enumerating objects, and counting in 2s, 5s and 10s from different multiples to develop their recognition of patterns in the number system for example, odd and even numbers , including varied and frequent practice through increasingly complex questions. They recognise and create repeating patterns with objects and with shapes.

They should realise the effect of adding or subtracting 0.

## Lesson Plan

This establishes addition and subtraction as related operations. Pupils combine and increase numbers, counting forwards and backwards. They discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly. Through grouping and sharing small quantities, pupils begin to understand: multiplication and division; doubling numbers and quantities; and finding simple fractions of objects, numbers and quantities.

## Year 2 Maths worksheets, lesson plans and other primary teaching resources

They make connections between arrays, number patterns, and counting in 2s, 5s and 10s. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole. The pairs of terms: mass and weight, volume and capacity, are used interchangeably at this stage. Pupils move from using and comparing different types of quantities and measures using non-standard units, including discrete for example, counting and continuous for example, liquid measurement, to using manageable common standard units.

In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers. Pupils handle common 2-D and 3-D shapes, naming these and related everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other. Pupils use the language of position, direction and motion, including: left and right, top, middle and bottom, on top of, in front of, above, between, around, near, close and far, up and down, forwards and backwards, inside and outside.

Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with movement on a clock face. Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least and solving a variety of related problems to develop fluency. They count in multiples of 3 to support their later understanding of a third. As they become more confident with numbers up to , pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.

They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand 0 as a place holder. Pupils extend their understanding of the language of addition and subtraction to include sum and difference.

This establishes commutativity and associativity of addition. Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers. Pupils use a variety of language to describe multiplication and division. Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other.

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They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition.

They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a non-unit fraction. Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line for example, 1 , 1 or 1 , 1 , 2.

This reinforces the concept of fractions as numbers and that they can add up to more than 1. Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations. Pupils become fluent in telling the time on analogue clocks and recording it. They become fluent in counting and recognising coins. Pupils handle and name a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons and cuboids, prisms and cones, and identify the properties of each shape for example, number of sides, number of faces.

Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read and write names for shapes that are appropriate for their word reading and spelling. Pupils draw lines and shapes using a straight edge. Pupils should work with patterns of shapes, including those in different orientations. Pupils record, interpret, collate, organise and compare information for example, using many-to-one correspondence in pictograms with simple ratios 2, 5, The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value.

This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them.

It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word-reading knowledge and their knowledge of spelling. Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and Using a variety of representations, including those related to measure, pupils continue to count in 1s, 10s and s, so that they become fluent in the order and place value of numbers to 1, Pupils practise solving varied addition and subtraction questions.

For mental calculations with two-digit numbers, the answers could exceed Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to 3 digits to become fluent see Mathematics appendix 1. Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency.

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8. Through doubling, they connect the 2, 4 and 8 multiplication tables. Pupils develop reliable written methods for multiplication and division, starting with calculations of two-digit numbers by one-digit numbers and progressing to the formal written methods of short multiplication and division. Pupils solve simple problems in contexts, deciding which of the 4 operations to use and why. These include measuring and scaling contexts, for example 4 times as high, 8 times as long etc and correspondence problems in which m objects are connected to n objects for example, 3 hats and 4 coats, how many different outfits?

Pupils connect tenths to place value, decimal measures and to division by They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to measure. Pupils understand the relation between unit fractions as operators fractions of , and division by integers. They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity. Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency. The comparison of measures includes simple scaling by integers for example, a given quantity or measure is twice as long or 5 times as high and this connects to multiplication.

Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts.

The decimal recording of money is introduced formally in year 4. Pupils use both analogue and digital hour clocks and record their times. In this way they become fluent in and prepared for using digital hour clocks in year 4. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.

Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts. Pupils understand and use simple scales for example, 2, 5, 10 units per cm in pictograms and bar charts with increasing accuracy. They continue to interpret data presented in many contexts. Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1,, including counting in 10s and s, and maintaining fluency in other multiples through varied and frequent practice.

They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far.

Two Step Word Problems - 3rd Grade Math Videos

They connect estimation and rounding numbers to the use of measuring instruments. Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of 0 and place value were introduced over a period of time. Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency see Mathematics appendix 1. Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency. Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers see Mathematics appendix 1.

Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or 3 cakes shared equally between 10 children. Pupils should connect hundredths to tenths and place value and decimal measure. They extend the use of the number line to connect fractions, numbers and measures. Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths.

Grace has 27 lollies for her party friends. She wants each friend to have 3 lollies. How many friends can she invite to her party? Now that we have established a structure across school that allows for children to use bar models for KS1 SATs, we are now ready to teach pupils how to use the bar model for a deeper understanding of complex problems during Key Stage 2 and particularly in preparation for KS2 SATs. The key question at any stage, at any age is what do we know?

preview.bluetangent.org/jetir-gree-manual.php By training pupils to ask this when presented with word problems themselves, they quickly become independent at drawing bar models. For example, in the problem: Egg boxes can hold 6 eggs. We need to fill 7 boxes. How many eggs will we need? We know that there will be 7 egg boxes, so we know we can draw 7 rectangular bars.

We know we need to find the amount of eggs we have altogether. We can see we will need to use repeated addition or multiplication to solve the problem. Bar Modelling is one of the key maths teaching strategies our tutors use to boost progress and raise confidence in Maths. As tutors progress through a lesson from the procedural to the more conceptual understanding of a topic, they will often use a bar model to assist a pupil to grasp a tricky concept or to break down a word problem. How much more does one orange cost than one lemon?

Some pupils will not need the bar model to represent the next stage, but if they do, they would calculate and then allocate the cost onto the model:. Then those pupils that needed this stage, should be able to see that to answer the question, they need to calculate 45p — 20p. With the answer of 25p. On Saturday Lara read two fifths of her book.

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On Sunday, she read the other 90 pages to finish the book. If we create our bar model for what we know:. In this final example, we look at how an equation can be demystified:. So each side of the equation will total The below model shows all sections completed. This is not necessary for the pupils to do, the representation is merely useful until they can see the steps necessary to calculate whatever they are faced with:. Now that you have seen how bar models can help pupils solve questions for the KS1 SATs and the KS2 SATs and you have a structure that can be put in place across the whole school to enable pupils to do so.